I am attaching the only source I know for this pedigree which comes from the book: Register of Maryland's Heraldic Families. I fear it must be taken w/ a grain of salt.
It is extremely hard to make any sense of this pedigree which has to be viewed as a 2nd hand source. I also have the Fairfax Pedigree wall chart from the Fairfax Soc. I have looked at this bef. to try and figure it out and just looked again.
The only way I can follow which agrees partially is:
Sir Thomas m. Ellen Aske
s/ Henry m. Mary Cholmley
s/ Henry m. Frances Barwick
It ends here bec. they had no son John. And of course Henry did not come to VA and MD.
They did have a son Henry b. at Bolton Percy whose son William was the Col Wm Fairfax who founded the VA Fairfax line. No son John who lived past infancy for this family.
This Bolton family is also not the Catholic family and the MD family was Catholic.
I fear this lineage without any first hand evidence to support it is pretty doubtful.